The Forcing Conundrum

Guest Post by Willis Eschenbach.

For all of its faults, the IPCC (Intergovernmental Panel on Climate Change) lays out their idea of the climate paradigm pretty clearly. A fundamental part of this paradigm is that the long-term change in global average surface temperature is a linear function of the long-term change in what is called the “radiative forcing”. Today I found myself contemplating the concept of radiative forcing, usually referred to just as “forcing”.

So … what is radiative forcing when it’s at home? Well, that gets a bit complex … in the history chapter of the Fourth Assessment Report (AR4), the IPCC says of the origination of the concept (emphasis mine):

The concept of radiative forcing (RF) as the radiative imbalance (W m–2) in the climate system at the top of the atmosphere caused by the addition of a greenhouse gas (or other change) was established at the time and summarised in Chapter 2 of the WGI FAR [First Assessment Report].

tropopause temperature by latitude

Figure 1. A graph of temperature versus altitude, showing how the tropopause is higher in the tropics and lower at the poles. The tropopause marks the boundary between the troposphere (the lowest atmospheric layer) and the stratosphere. SOURCE 

The concept of radiative forcing was clearly stated in the Third Assessment Report (TAR), which defined radiative forcing as follows:

 The radiative forcing of the surface-troposphere system due to the perturbation in or the introduction of an agent (say, a change in greenhouse gas concentrations) is the change in net (down minus up) irradiance (solar plus long-wave; in Wm-2) at the tropopause AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.

In the context of climate change, the term forcing is restricted to changes in the radiation balance of the surface-troposphere system imposed by external factors, with no changes in stratospheric dynamics, without any surface and tropospheric feedbacks in operation (i.e., no secondary effects induced because of changes in tropospheric motions or its thermodynamic state), and with no dynamically-induced changes in the amount and distribution of atmospheric water (vapour, liquid, and solid forms).

So what’s not to like about that definition of forcing?

Well, the main thing that I don’t like about the definition is that it is not a definition of a measurable physical quantity.

We can measure the average surface temperature, or at least estimate it in a consistent fashion from a number of measurements. But we can never measure the change in the radiation balance at the troposphere AFTER the stratosphere has readjusted, but with the surface and tropospheric temperatures held fixed. You can’t hold any part of the climate fixed. It simply can not be done. This means that the IPCC vision of radiative forcing is a purely imaginary value, forever incapable of experimental confirmation or measurement.

The problem is that the surface and tropospheric temperatures respond to changes in radiation with a time scale on the order of seconds. The instant that the sun hits the surface, it starts affecting the surface temperature. Even hourly measurements of radiative imbalances reflect the changing temperatures of the surface and the troposphere during that hour. There is no way that we can have the “surface and tropospheric temperatures and state held fixed at the unperturbed values” as is required by the IPCC formulation.

There is a second difficulty with the IPCC definition of radiative forcing, a practical problem. This is that the forcing is defined by the IPCC as being measured at the tropopause. The tropopause is the boundary between the troposphere (the lowest atmospheric layer, where weather occurs), and the stratosphere above it. Unfortunately, the tropopause varies in height from the tropics to the poles, from day to night, and from summer to winter. The tropopause is a most vaguely located, vagrant, and ill-mannered creature that is neither stratosphere nor troposphere. One authority defines it as:

The boundary between the troposphere and the stratosphere, where an abrupt change in lapse rate usually occurs. It is defined as the lowest level at which the lapse rate decreases to 2 °C/km or less, provided that the average lapse rate between this level and all higher levels within 2 km does not exceed 2 °C/km.

This is an interesting definition. It highlights that there can be two or more layers that look like the tropopause (little temperature change with altitude), and if there is more than one, this definition always chooses the one at the higher altitude.

In any case, the issue arises because under the IPCC definition the radiation balance is measured at the tropopause. But it is very difficult to measure the radiation, either upwelling or downwelling, at the tropopause. You can’t do it from the ground, and you can’t do it from a satellite. You have to do it from a balloon or an airplane, while taking continuous temperature measurements so you can identify the altitude of the tropopause at that particular place and time. As a result, we will never be able to measure it on a global basis.

So even if we were not already talking about an unmeasurable quantity (radiative change with stratosphere reacting and surface and tropospheric temperatures held fixed), because of practical difficulties we still wouldn’t be able to measure the radiation at the tropopause in any global, regional, or even local sense. All we have is scattered point measurements, far from enough to establish a global average.

This is very unfortunate. It means that “radiative forcing” as defined by the IPCC is not measurable for two separate reasons, one practical, the other that the definition involves an imaginary and physically impossible situation.

In my experience, this is unusual in theories of physical phenomena. I don’t know of other scientific fields that base fundamental concepts on an unmeasurable imaginary variable rather than a measurable physical variable. Climate science is already strange enough, because it studies averages rather than observations. But this definition of forcing pushes the field into unreality.

Here is the main problem. Under the IPCC’s definition, radiative forcing cannot ever be measured. This makes it impossible to falsify the central idea that the change in surface temperature is a linear function of the change in forcing. Since we cannot measure the forcing, how can that be falsified (or proven)?

It is for this reason that I use a slightly different definition of the forcing. This is the net radiative change, not at the troposphere, but at the TOA (top of atmosphere, often taken to mean 20 km for practical purposes).

And rather than some imaginary measurement after some but not all parts of the climate have reacted, I use the forcing AFTER all parts of the climate have readjusted to the change. Any measurement we can take already must include whatever readjustments of the surface and tropospheric temperatures that have taken place since the last measurement. It is this definition of “radiative forcing” that I used in my recent post, An Interim Look at Intermediate Sensitivity.

I don’t have any particular conclusions in this post, other than this is a heck of a way to run a railroad, using imaginary values that can never be measured or verified.

w.

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Pamela Gray
December 16, 2012 10:43 am

Ocean heating: The Coriolis affect combined with surface obstacles and currents define the major components of Earth’s unique oceanic fluid dynamics. Ocean layers are heated, especially around the equatorial belt, with IR heating (not long wave) which itself is filtered to various levels at the surface because of cloud variation. The heat absorbed by the oceans is then mixed and sloshed around or allowed to sit and layer calmly via trade wind variations.
Oceanic heat loss: My educated guess is that in various ways, heat is largely released back into the atmosphere, sometimes because of storms, and usually because of its eventual trip to the poles where it evaporates and eventually escapes the confines of our planet. Some years and decades (long and short) the oceans lose a lot of heat, and some years and decades that cooling system doesn’t work so well. This gain/loss see-saw is anything but predictable.
I think longwave radiation oceanic heating (the kind that is re-emitted from the ocean and re-emitted back into the ocean from the atmosphere) is a tiny player, buried in the noise, in the above description, and certainly not at all in measurable trends.

Frank
December 16, 2012 11:11 am

Phi replied to me: “Well, science is not the stock market! Either radiative forcing has a meaning, or it does not.”
The IPCC’s definition of radiative forcing provides a very clear meaning. Radiative forcing is the result of a calculation that determines how the net flux of radiation through the atmosphere is expected to change as the atmosphere and/or the radiation entering the atmosphere changes. The IPCC has specified where (the tropopause) and how (allow stratosphere to reach radiative equilibrium) that calculation is to be done, and their choices make sense. To do the calculations, one needs carefully measured parameters from many reproducible laboratory experiments, atmospheric conditions and composition, and how much radiation enters the atmosphere from the sun, the surface and cloud tops. (All but the parameters change from location to location, so there is no single correct answer.) At least some of the software for doing these calculations is available on the Internet. If anything in climate science desires to be called “settled science”, it might be radiative forcing.
Unfortunately, “radiative forcing” reported in W/m2 doesn’t mean anything to non-specialists. The IPCC chapters that I have read about GHG forcing don’t tell the public how to interpret radiative forcing in terms of a temperature increase. Instead they wait until they have amplified radiative forcing with poorly understood feedbacks to produce climate sensitivity or processed through climate models containing parameters that have been tuned so that 20th century warming is attributed to increasing GHGs.
Here’s a reasonable interpretation of radiative forcing in terms of warming, generally called the no-feedbacks climate sensitivity. W = eoT^4, so W+dW = eo(T+dT)^4 where dW and dT are small changes, deltaW and deltaT. With a little algebra and ignoring terms with higher powers of dT, one can derive an equation I rarely encounter: dW/W = 4*(dT/T). It says that the percent change in radiation will be four times bigger than the associated percent equilibrium change in temperature (in degK). To compensate for a radiative forcing of 3.7 W/m2 (1.54% change) we need a 0.38% increase in temperature. Since the surface and lower troposphere receive about 240 W/m2 of solar radiation (after account for albedo), the equivalent blackbody temperature (255 degK) appears to be the most relevant temperature to use, affording a 1.0 degK warming. Where will this warming take place? Calculations can’t tell us, but 90% of the photons escaping to space are emitted from the upper troposphere, so a reasonable answer is that upper troposphere (where the temperature is near 255 degK) will warm 1.0 degK. If the lapse rate remains unchanged, the surface will warm by 1.0 degC too.

Mack
December 16, 2012 11:56 am

Willis says……..Dec15th 201 7.28pm
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Everything you say is IF there Willis. Did Micheal Moon say you worked as a massage therapist? Probably explains why you you were asking everybody for a bit of traction further up .

phi
December 16, 2012 12:37 pm

Frank,
“If anything in climate science desires to be called “settled science”, it might be radiative forcing.”
How is computed the CO2 forcing? By adding with a thought experiment some CO2 created ex nihilo. What is the temperature of this CO2? Obviously not defined. We uses the temperature profile of the atmosphere before the add but it’s a perfectly arbitrary operation. It is absolutely necessary to leave the new CO2 to adapt to its environment before making any calculation. Unfortunately, the principle of radiative forcing requires an instantaneous balance. This calculation is actually under-determined and the value obtained arbitrary.
We can being aware of that also considering the schematic equation of heat transfer through the atmosphere: Ts = L * P + k * P ^ 0.25 where Ts is the surface temperature, P the heating power, L and K synthetics factors. The addition of CO2 occurs in L and can not be modeled by an alteration of P. There is an exception with the energy evacuated directly from the ground and now intercepted by the added CO2 but it is a small amount.
“If the lapse rate remains unchanged, the surface will warm by 1.0 degC too.”
1 ° C may be correct as an average, by cons, we know that it’s not valid for surface because the main effect of the added CO2 is to change the lapse rate by reducing the potential radiative losses along the column.
This warming being not valid at the surface is critical because it is the surface temperature that initiates the feedback on water vapor.

Greg House
December 16, 2012 1:40 pm

Willis Eschenbach says, December 16, 2012 at 9:55 am: “While NET heat flow always goes from hot to cold as you claim, with radiation there are always two flows of energy going on. There is a flow of energy from the warmer to the cooler area, and there is also a flow of energy from the cooler to the warmer area. It is only the NET flow that is constrained to always go in one direction. Get a college-level beginner’s physics book, they’ll cover it in there. Here’s an example illustration, from the University of Sydney.”
============================================================
Willis, your illustration does illustrate an IDEA, but like any other illustration it does not prove the idea to be right or to be a scientific fact. You illustration only demonstrates that there are other people who share your idea about “NET”.
Second, and this is important, this “NET” thing makes physical sense with regard to temperature only, if “a flow of energy from the cooler to the warmer area”, as you put it, has an effect on the temperature of the warmer area. If it does not, your “NET” does not make physical sense at all.
Even if there is some effect on the temperature of the warmer area, but this effect is disproportionately or even vanishingly small, you can not just add or subtract energy and then derive temperature from the result of this arithmetic operation. This would be no science.
Which means, until this “NET” thing is not proven experimentally, it remains a pure fiction.
Please, Willis, present a clear reference to and a description of a REAL scientific experiment (not just a “thought experiment”) proving your idea about this “NET” effect.

December 16, 2012 5:35 pm

Willis writes “For TimTheToolMan and the others who think that downwelling longwave radiation can’t warm the ocean, not one single one of you has answered my simple question.”
I do think DLR slows the rate of cooling, Willis. I’ve told you this a number of times in the other thread. I’ve not said it doesn’t in this or any other thread so I dont know where that accusation keeps coming from.
I am pointing out they so far I believe your understanding on how the ocean warms as a result is lacking. You’ve stated that there is no difference between warming and slower cooling but then you’ve made statements that clearly indicate you believe the DLR increases the SST. Directly!. It does not. It cant because the ocean is cooling Willis. The sun warms it at depth, not at the very surface when, for example, clouds come over.
There IS a difference between slower cooling and warming because when you think “warming”, when you think more DLR means +100 W/m2 you can and do get it wrong.

jae
December 16, 2012 5:58 pm

Willis notes:
“Greg, I doubt you can find what you are asking for. Such basic statements are rarely accompanied by experiments. The fact that solid objects radiate depending on their temperature is such basic science that it is presented as a statement of fact rather than with an experiment.’
BUT, sir, I think I just gave you THE experiment (Phoenix vs. Atlanta). The amount of radiation from greenhouse gases seems to matter very little, if at all. Water and water vapor can probably explain it all.
I noticed that you have not responded to my last comment on this subject, and I am wondering why…

December 16, 2012 5:58 pm

I don’t know anyone who disputes the fact that things with mass and temperature radiate (except perhaps Myrhh, I’m not sure what he or she thinks). The Kent drawing shows two independent sources radiating toward each other. No problem. Going further, I don’t know anyone disagreeing with the idea of a passive receptor heating up and radiating. The problem is trying to do useful work with re-radiated energy…and in the presence of convection? Good luck. You can’t get an average temperature increase of 33C from backward atmospheric re-radiation. Something this blatant would be easy to instrument in a lab environment.

JazzyT
December 16, 2012 6:58 pm

There seems to be some confusion about the idea of GHGs emitting IR which is absorbed at the surface, and heating it. It might be better to say, “transferring heat to the surface” rather than “heating the surface” because, at night, in the absence of other effects, the surface will inevitably cool, but will cool more slowly than without the GHGs. During the day, the surface is warmed by the sun.
The whole climate change issue involves questions of whether the Earth might warm, on the average, by 2 degrees C over the next century, or by 3 degrees, perhaps 5 degrees, or by 1 degree or less, with various consequences or lack thereof.. This projected temperature change, over a century, is superimposed on daily and seasonal changes. Daily changes of 10 degrees is quite ordinary, and seasonal changes of 30 degrees or more are quite common, as compared to a much smaller AVERAGE change over 100 years.
There is NO need to worry about where the heat would come from for global warming; it comes in every day. If the Earth were to heat up, on the average, by 10 degrees C over the next century, most climate scientists think that truly cataclysmic results would follow–but NOBODY thinks that this is a remotely serious possibiltiy. The balance between incoming and outgoing energy is fine enough that one day’s sunlight changes the temperature much more than any average change that anyone seriously considers for the next century. (Heating the top layers of the oceans would take more than a day, but still much shorter than a century.)
GHGs do indeed radiate IR to the surface and transport heat thereby. But the surface cannot actually warm from this unless the atmosphere is actually warmer (which could happen if, say, a warm front moves through). But the effect of GHGs is to slow the rate at which the surface cools through IR emission. The actual mechanism is complicated, but that’s the end result.
We could try to calculate the temperature at the surface in terms of how much the atmosphere radiates to the ground, various heat capacities, etc. but that’s difficult to conceive of, and difficult to solve. There’s an easier way: despite the differences of night and day, seasons, weather, etc. the incoming and outgoing energy is always very close to balanced. Were this not so, the average temperature would go up, not over a century, but over a matter of weeks or days. It would probably be very exciting. But the main regulatory mechanism, the sharp dependence of IR emission on temperature, puts the brakes on quickly. As Frank mentioned above, emission goes as the fourth power of temperature. For every 1% increase in absolute temperature, which is about 3 degrees C, there’s about a 4% increase in IR emission. So, if nothing else has changed, that cools the surface down pretty quickly. (For a demo, wait until sunset.)
So, to solve it the easy (or easier) way, we look at the percentage of IR that gets through (at each wavelength, it’s not quite simple) and then ask: what temperature would the surface have to be so that the heat that escapes through IR in 24 hours is equal to the heat received from the sun in one day? The more the GHGs “block” the IR the higher that temperature is. The word “block” is a gross oversimplirication, but in the end, that’s why the temperature goes up–more solar heat is retained, until the surface is warm enough to shove through an amount of energy that equals, on the average, what the sun puts in.
Of course, after that, you look at the IR absorption spectra of the greenhouse gases, blackbody emission spectra, heat transport through air, currents, ocean currents, evaporation, precipitation, thermals caused by politicians emitting large amounts of hot air…lots of complications. But one thing you DON”T have to worry about is how the energy gets to the ground to heat it up. The sun takes care of that, every day.

Greg House
December 16, 2012 10:22 pm

Willis Eschenbach says:, December 16, 2012 at 5:23 pm: “Greg, […] The fact that solid objects radiate depending on their temperature is such basic science that it is presented as a statement of fact rather than with an experiment.
Here is some information from MIT on exactly how to calculate the radiative heat exchange between two surfaces. They have no doubt that there are two separate radiative flows.
Now, if you don’t believe what the folks at MIT say about radiation, I’m afraid you’ll have to take it up with them.”

=====================================================
Willis, I am not questioning the fact that solid objects radiate depending on their temperature, or that there are separate radiative flows. You have probably misunderstood the point. I am questioning the alleged effect of radiation from colder bodies on TEMPERATURE of warmer bodies, and logically the calculations of what you call “NET” transfer. I hope you have understood the point now.
Your references to “folks at MIT” are not a scientific argument unfortunately, anyway not when the very essence of your point is questioned. It is a wide spread logical fallacy called “appeal to authority”. I am very sure that “folks at MIT” can give references to other “folks” and so on. Such a circle of references is, however, not a scientific argumentation.
You are apparently a knowledgeable man, so I guess, if you can not refer to a real scientific experiment confirming your (and other “folks’) assertion about that “NET” thing, you probably are capable of understanding that this assertion can not be considered a scientific fact, it is just a fiction.

December 16, 2012 10:55 pm

So here’s a stab at explaining why the oceans don’t freeze for lack of DLR:
Take a water heater and remove the dip tube. Install a big pump that recycles water between the holes at the top of the tank. What you are doing is installing a flowmeter and thermometer on the outflow side and saying, “Wow, there is so much energy leaving this thing would freeze if it weren’t warmed by water coming back in.”…

December 16, 2012 11:27 pm

Willis writes “Here’s the thing. There’s no difference in result between the blanket and the torches.”
You’ve made another strawman argument without even realising it… The thing is that DLR (and a blanket) redirects the object’s energy back at the object. Back radiation. And its just not possible for a blanket to make the block of iron warmer than when you started. Just because you can set a propane torch up to account for the same energy loss means nothing and doesn’t mean warming is the same as cooling.
Do you stand by this statement that you made to tallbloke?
“The very surface warms … until it’s slightly warmer than the bulk … which then heats up slightly, until the surface is slightly cooler than the bulk, and the previous condition (cooler surface) is restored.”
Because this is very explicitly saying that DLR can warm the ocean warmer than it was before you started. This is like saying I can put a blanket on the iron or put coffee in a thermos and it will get warmer than when I started.

AlecM
December 16, 2012 11:34 pm

Willis says this: ‘Regarding heat flow, you are missing the boat entirely. While NET heat flow always goes from hot to cold as you claim, with radiation there are always two flows of energy going on. There is a flow of energy from the warmer to the cooler area, and there is also a flow of energy from the cooler to the warmer area. It is only the NET flow that is constrained to always go in one direction. Get a college-level beginner’s physics book, they’ll cover it in there. Here’s an example illustration, from the University of Sydney.’
This is plain wrong. Unfortunately most people are taught it as if it’s correct. The reason is they are taught the S-B equation and the difference, net energy flux is the difference between the two S-B predictions. This is incredibly misleading though and you along with most have fallen in to the trap.
To prove this you go back two steps in the physics. The first is the Planck Irradiation Function which when integrated over the wavelengths or the wave numbers is the S-B equation. The second is to understand the the PIF at any wavelength/wave number is for a collimated beam identical to the Poynting Vector. This transfers to physics to Maxwell’s Equations.
The wonder of this is Poynting’s Theorem which is that the net PV at any point in space is the vector sum of all the arriving PVs. In other words there can never be two streams doing work. Only the vector sum at a point can do work.
This is why the climate models are total, absolute bunkum. You can’t compute absorption of energy from the two streams because it exaggerates warming by a factor of ~7. What’s more as there is zero net CO2 IR emitted from the surface [basic radiation physics at thermal equilibrium means net PV is zero where the two PVs are near black body iamplitude] there can never be any CO2-AGW or positive feedback.
Please Willis, learn the real physics and tell these IPCC charlatans they have got it wrong. It goes back to Houghton using the two-stream approximation to calculate energy absorption. If he had had the scientific wit to work out that the DOWN warming is negative to offsets most of the UP warming we might have avoided this incredible mess of fake science.

AlecM
December 17, 2012 12:17 am

I shall also add a point I haw made in the past which is that the belief in DLR is entirely baseless because a pyrgeometer measurement is the artefact of the instrument’s shielding. The proof it to have two pyrgeometers back to back in zero temperature gradient – net signal = 0. Take one away and the signal jumps to a measure of the S-B flux for that body at its particular temperature and emissivity.
However, until that electromagnetic wave combines destructively with the wave from the opposite direction, it cannot do any thermodynamic work. ‘Back radiation’ is an imaginary energy flow all of which is destroyed at the Earth’s surface. The only work that can be done from the Earth’s surface is the 63 W/m^2 net IR flux, the 17 W/m^2 convection and the 80 W/m^2 evapo-transpiration.
Anyone who claims differently has to justify it from Maxwell’s Equations and they can’t.

AlecM
December 17, 2012 12:47 am

Willis: The citation you reference, about radiative heat transfer calculations, is exactly what I was taught as a Metallurgical Engineer. Until 3 years’ ago when I set out to study exactly what the IPCC claimed, I have never thought beyond the S-B analysis. However, once I realised the climate models have in them a perpetual motion machine, creating much more IR energy to be absorbed than real net IR, I decided to find out why.
The two-stream approximation cannot be used to calculate heat absorption unless one stream is defined as negative, the cooler to the warmer. You cannot have a perpetual motion machine. Unfortunately, the grant money would disappear because the CAGW scare vanishes, and we can’t have real science interfering with capitalism, can we?

Mack
December 17, 2012 12:51 am

Dec 14th @10.34 am “So what is providing…….. energy that is keeping the ocean from freezing? I keep waiting and waiting for you folks to say it is not DLR to explain why the oceans are not frozen” (then later)… “where is the energy coming from to keep them unfrozen?”
So then he ,Willis (hopefully) reads what I said to him about Trenberth’s unreal geometrically derived IPPC crap of 160w/sq.m. reaching the Earths surface. But no he persists..2 days later..
Dec16th 2012 @6.38pm “So the problem remains- the sun alone is not enough to keep it liquid”.
You know how you might be reading something right in front of you but cannot believe what your eyes are seeing. This is exactly my case here. How can this guy Willis who calls himself a scientist (maybe that’s his problem) say such stuff.
Willis…
If you were to take the earth and for hypothesis sake freeze the seas. Then introduce a sun which will apply a continuous and timeless input of energy to the surface of 340w/sq.m. I’m sure that before too long we would approach what we have today in reality. I’m going to say this again Willis without any smilies or winkies . It’s the sun stupid.

AlecM
December 17, 2012 1:00 am

Willis: ‘If DLR is not keeping the ocean from freezing, what is?’
The answer is very simple. The oceans do not emit 400 W/m^2 ULR. The only IR they emit is the net 60 W/m^2. This is an inescapable fact – only net energy flows are real.

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